Animating a rotation but with acceleration
Unfortunately, the cycles modifier can't be set to repeat only a certain part of the action. You have two alternatives.

Linear Extrapolation

Press Shift+E and choose Linear Extrapolation. This way the wheel will keep rotating based on the last two keyframes up to infinity.

Use Non Linear Animation

Go to the NLA editor. Press the down button. The active action will be converted to an action strip. I have duplicated the action strip with Shift+D and moved it to the frame, where the original strip ends.

With the second strip selected, we can set it to the original action, if a duplicate action was made, although this is not necessary.Set the Start Frame to your second keyframe, frame which one one the wheels rotation has reached its final speed. Set the End Frame to the last keyframe. Set the repeat scale as desired.This way the linear motion of the action is isolated and repeated.